It is a ratio of the width. 40% of 225 mm v 45% of 225 mm. Are you just having the tires swapped on the original wheels? Better for winter tires would be something like a 215 on a 17" wheel or even a 215 on the 18" wheel. Narrower gets through the snow better.

+1

17" snows are cheaper as well.
the cost of mounting and balancing twice a year (if you plan on just swapping tires) pays for new 17" rims in about 2.5 years